LDR 02179     2200253   4500
010    _a9783540668091
011    _a1617-9692
090    _a14032
101    _aeng
100    _a20181212              frey50       
200    _aElemental methods in ergodic Ramsey theory
       _fRandall McCutcheon
210    _aBerlin
225    _9180169
       _aLecture notes in mathematics
300    _aThis book gives an overview over the main results of chromatic and density Ramsey theory in ℤ. It is based on lecture notes for a graduate course and therefore additionally provides a large variety of exercises and problems that are helpful for a better understanding of the field. Even though many of the presented results were originally proven combinatorially, most of the proofs in this book are based on topological dynamics and ergodic theory. The problems considered mainly fall into the classes of van der Waerden type theorems, Hindman type theorems and Szemerédi type theorems. After an introduction to Ramsey theory and to topological dynamics in the first chapter, results from infinitary Ramsey theory and density Ramsey theory are presented in Chapters 2 and 3. In Chapters 4 and 5 ergodic theory is used to establish double recurrence results and multiple recurrence results. In particular, Roth theorems and Szeméredi theorems are proven in this context. (Zentralblatt)
686    _20
       _bCombinatorics -- Extremal combinatorics
       _xRamsey theory
686    _20
       _bGeneral topology -- Connections with other structures, applications
       _xTopological dynamics
686    _20
       _bMeasure and integration -- Measure-theoretic ergodic theory
       _xMeasure-preserving transformations
686    _20
       _bDynamical systems and ergodic theory -- Ergodic theory
       _xMeasure-preserving transformations
700    _4070
856    _uhttp://link.springer.com/book/10.1007/BFb0093959
856    _uhttp://zbmath.org/?q=an:0945.05063
856    _uhttp://www.ams.org/mathscinet-getitem?mr=1738544
905    _aaw
001     14032
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